The only thing that is known right now is that once system is colonized - standard rules of BGS applied. How exactly system is populated with more MFs than just the one player bought a beacon from is unknown. In current BGS rules there is a limit on a distance to which MFs can expand, don't know how long it is, but probably not even a 100 Ly.Well... passenger missions are linked to BGS factions, so the numer of passengers you take can add to the BGS population. New missions for 'we need (agg/tech/extraction/etc) expert in the colony, take them and their family... also need cargo space for their stuff' but maybe that's factored in to passenger berths.
I don't know how BGS expands into new systems by default, so shrug
Also, in current BGS rules - nothing apart from Thargoids can change system population. Obviously this part will be changed, as colonized systems need to grow somehow. For initial colonists and construction crews - it is probably safe to assume that distance to where the colonization ship would take them won't be any problem.
For the regular population - well, I doubt that there would be much desire to go somewhere where there is little to no infrastructure and basic comforts of life. Even to escape Thargoids, because living in a very remote systems is not really much safer, especially if it is closer to Thargoids territory, and in addition - in case of trouble chances to relocate somewhere safer are a lot smaller than in a vicinity of the Bubble.
Passenger missions could influence population, if even by relatively small numbers, it makes sense, and shouldn't be hard to implement. But that would probably work both ways - passengers in +population, passengers out -population. Architect would most likely only add, but it could be fun to steal population from somebody and basically shut down their system.
In any way - things like that are extra mechanics, and they would need to be interconnected with other mechanics, or at least account for their possible effects. With how complex Colonisation already is, I doubt that such intricate details and mechanics would be developed in current iteration.